Mathematical board game

ABSTRACT

An instructive board game combining solving mathematical questions and making moves on a board in the manner of the well-known game of Tic Tac Toe is disclosed. The board displays mathematical values to be used in an operation in one location, and possible mathematical results in an array at another location. After one player selects a mathematical value, another player selects another mathematical value which will when subjected to the operation, will yield a mathematical result corresponding to a result shown at a desired location on the board. The second player then occupies that location. Players attempt to occupy abutting locations arranged three in a row, vertically, horizontally, or diagonally. In one implementation, the game gives players practice in solving quadratic equations.

FIELD OF THE DISCLOSURE

The present disclosure relates to educational board games, and more particularly, to an educational board game wherein making a move is predicated on performing a mathematical operation.

BACKGROUND

The world of mathematics can be daunting to new students. In particular, mathematical operations beyond simple addition, subtraction, multiplication, and division using whole numbers may be regarded as impenetrable by beginners. This can lead to slowed or even non-existent mastery by students.

There exists a need for a mechanism to encourage new students to become familiar with mathematical operations, so that psychological barriers to mastery are overcome.

SUMMARY

The present invention contemplates a game which has as a consequence familiarity with certain mathematical operations. The actual game elements utilize mathematical calculations, yet are not inherently mathematical. Therefore, the game can be presented as a game, with mathematical aspects being delegated to secondary status. This may encourage students to play the game, thus becoming familiar with mathematic elements and related operations. Hence, the student may be more susceptible to self-teaching, and will not be put off by apparent impenetrability of the mathematic aspect.

To this end, the novel game contemplates displaying mathematical terms such as a combination of a numerical integer and an abstract unknown, the latter typically presented in alphabetical format.

The game is played by having a first player select a combined integer and abstract unknown. A second player selects a second combined integer and abstract unknown. The combined selections are used in an arithmetic operation, such as pertaining to quadratic equations. Potential answers are displayed on a playing board. A space displaying the appropriate answer for the arithmetic operation is then occupied by a token representing the second player.

Game play described thus far is repeated until a player occupies a requisite number of vertically adjacent spaces, horizontally adjacent spaces, or diagonally adjacent spaces. The game may simulate the well-known game of Tic Tac Toe, in which each player attempts to occupy three spaces adjacent vertically, horizontally, or diagonally. Ordinarily, the other player will attempt to block a successful succession of occupied spaces. In the present game, with the bigger board than Tic Tac Toe, the game may continue beyond the first succession of three occupied spaces.

Game strategy requires players to calculate a number of results of the arithmetic operation, thereby forcing the players to become familiar and comfortable with integer/abstract unknown elements. Although not represented as the scored result of the game, the latter is actually the true point of the game.

BRIEF DESCRIPTION OF THE DRAWINGS

Various objects, features, and attendant advantages of the disclosed concepts will become more fully appreciated as the same becomes better understood when considered in conjunction with the accompanying drawings, in which like reference characters designate the same or similar parts throughout the several views, and wherein:

FIG. 1 is a representation of a game board for use with a board game, according to at least one aspect of the disclosure;

FIG. 2 is a diagrammatic simplification of the game board of FIG. 1;

FIG. 3 is a diagrammatic simplification of the game board of FIG. 1, showing occupancy of a game board space after an exemplary first move by a player;

FIG. 4 is similar to FIG. 3, but shows an exemplary second move, made by a second player;

FIG. 5 is similar to FIG. 4, but shows additional exemplary moves made by both the first and second players;

FIG. 6 is similar to FIG. 5, but shows a further exemplary move made by the second player;

FIG. 7 is similar to FIG. 6, but shows a still further exemplary move made by the first player; and

FIG. 8 is similar to FIG. 7, but shows still another exemplary move made by the second player.

In FIGS. 2-8, numeric values shown in FIG. 1 which are irrelevant to the example being discussed are omitted for clarity of the view.

DETAILED DESCRIPTION

Referring first to FIG. 1, according to at least one aspect of the disclosure, there is shown a game board 100 including a row 102 of selectable numeric values and a matrix 104 of resulting numeric values which would result from multiplying two of the selectable numeric values of row 102. Those schooled in mathematics will recognize that the selectable numeric values of row 102 and the resulting numeric values shown in matrix 104 pertain to quadratic equations.

By way of simplified explanation, the game played using game board 100 in some ways simulates the game of Tic Tac Toe. However, rather than have players directly choose board spaces to occupy, the players are obliged to perform a mathematical operation which will result in authorization to occupy a desired board space. That is, correct calculation of the mathematical operation will authorize that player making the correct calculation to occupy that board space displaying the resulting numeric value arising from the calculation.

Stated in generic or abstract terms, there is shown a method of playing a board game having board positions presented as occupiable spaces. The method may comprise displaying a choice of selectable numeric values and performing a plurality of reiterative game operations. Each individual reiterative game operation of the plurality of reiterative game operations comprises having a first player select a first selectable numeric value, having a second player select a second selectable numeric value, performing a mathematical operation utilizing the first selectable numeric value and the second selectable numeric value, displaying a plurality of resulting numeric values each in one of the occupiable spaces, wherein each one of the resulting numeric values is a mathematical result of performing the mathematical operation using a unique two of the selectable numeric values, and designating that occupiable space having therein the resulting numeric value particular to the first selectable numeric value and the second selectable numeric value as being occupied by the second player. The method may further comprise performing additional ones of the reiterative operations, wherein roles of the first player and the second player are exchanged in each of the additional ones of the reiterative operations, and each of the occupiable spaces occupied by the first player and the second player is maintained as so occupied throughout each one reiterative operation, until one of the first player and the second player has occupied a predetermined array of adjacent occupiable spaces. The method may further comprise recognizing as a winner of each reiterative game operation that player having occupied the predetermined array of adjacent occupiable spaces, summing the number of occupied predetermined arrays for each of the players, and declaring as a winner of the game that player having the greatest number of occupied predetermined arrays.

Unless otherwise indicated, the terms “first”, “second”, etc., are used herein merely as labels, and are not intended to impose ordinal, positional, or hierarchical requirements on the times to which these terms refer. Moreover, reference to, e.g., a “second” item does not either require or preclude the existence of, e.g., a “first” or lower-numbered item, and/or, e.g., a “third” or higher-numbered item.

Board positions refer to occupiable spaces 106. Each occupiable space 106 may have indicia appearing thereon, such as the numeric values shown. Occupying a space may be performed for example by playing a token thereon. Tokens are not literally shown, but are shown representatively in FIGS. 3-8, as will be further described hereinafter.

In any one of the reiterative game operations, the first player selects the first selectable numeric value from row 102. Play then passes to the second player, who determines which occupiable space 106 he or she wishes to occupy, then performs the mathematical operation which would result in the resulting numeric value which appears on the desired occupiable space 106A.

For example, and also referring to FIG. 3, the first player selects a value “x−4” 108. The second player must then determine that the value “x+1” 110, when multiplied with the value “x−4” 108, will result in resulting numeric value “x²−3x−4” 112. As shown in FIG. 3, the second player then places a token 114 representing the second player on that occupiable space 106 bearing the legend “x²−3x−4” 112. In this example, a combination of selection of selectable numeric value “x−4” 108, followed by the calculation by the second player resulting in identifying the selectable numeric value “x+1” 110, and placement of a token on occupiable space 106 bearing the legend “x²−3x−4” 112 constitutes the basic reiterative game operation. In subsequent reiterative game operations, roles of the first and second players are periodically exchanged so that the first player is given an opportunity to occupy a desired occupiable space 106.

Exchange may be performed in any desired way. For example, in one implementation of the method of play, the step of performing additional ones of the reiterative operations comprises alternating respective roles of the first player and the second player in each subsequent iteration of the reiterative operations. However, if it is felt that undue advantage may accrue to one particular player, exchange may be modified for example such that the same player plays one role twice in succession, thereafter reverting to simple alternation. In another example, one player make take two turns at the first role, followed by the second player taking three turns at the second role.

Returning to the example of play, and also referring to FIG. 4, roles have been exchanged, and the first player has now calculated which selectable numeric value will combine with the selectable numeric value selected by the second player to yield a result corresponding to a resulting numeric value of an occupiable space 106B. The first player may then place his or her token 116 on occupiable space 106B.

Play continues at least until the first player or the second player has occupied a predetermined array of adjacent occupiable spaces 106. This is shown in FIG. 5, where play has advanced well beyond play illustrated in FIG. 4. As indicated by broken line 118, which will not literally appear in actual play, the first player has occupied three diagonally adjacent occupiable spaces 106B, 106C, 106D, placing additional tokens 116 on those occupiable spaces 106B, 106C, 106D. The second player has occupied another occupiable space 106E, blocking extension of the diagonally adjacent occupiable spaces 106B, 106C, 106D occupied by the first player. In most versions of the game, it will now be the turn of the second player.

FIG. 6 shows a possible move by the second player, who has now occupied an occupiable space 106F. FIGS. 7 and 8 show further move and countermove by the two players, the countermove not only partly blocking two horizontally adjacent occupiable spaces 106D, 106G, but threatening to establish occupiable spaces 106E, 106G and 106F, 106H as future diagonal rows of three.

In the method of play, the predetermined array of adjacent occupied spaces (e.g., 106B, 106C, 106D) may comprise three adjacent spaces 106 of the board game arranged in a straight line. Additionally, the three adjacent spaces 106 may be arranged serially in a horizontal row of the board game, arranged serially in a vertical column of the board game, or arranged serially in a diagonal row of the board game.

As hinted at previously, the step of performing the mathematical operation utilizing the first selectable numeric value and the second selectable numeric value may comprise generating and solving quadratic equations.

In the method of play, at least one the selectable numeric values and at least one of the resulting numeric values comprise an integer and a symbolic value of indeterminate magnitude, conventionally represented in mathematics and herein as “x”.

A win may be predicated on scores based on one or more predetermined arrays (e.g., three occupiable squares in a row occupied by one player). Given magnitude of matrix 104, a player may have a number of arrays, and may have more than three occupiable squares in a row.

It is contemplated that the novel game disclosed herein will be for the benefit of students learning mathematics. These students may vary considerably in age and ability. Therefore, scoring schemes may be varied to account for variations in age and ability. At the most junior level, attainment of the first row or predetermined array may end the game. At more advanced levels, play may continue until a great many predetermined arrays have been established by the players.

It should be understood that the various examples of the apparatus(es) disclosed herein may include any of the components, features, and functionalities of any of the other examples of the apparatus(es) disclosed herein in any feasible combination, and all of such possibilities are intended to be within the spirit and scope of the present disclosure. Many modifications of examples set forth herein will come to mind to one skilled in the art to which the present disclosure pertains having the benefit of the teachings presented in the foregoing descriptions and the associated drawings.

Therefore, it is to be understood that the present disclosure is not to be limited to the specific examples presented and that modifications and other examples are intended to be included within the scope of the appended claims. Moreover, although the foregoing description and the associated drawings describe examples of the present disclosure in the context of certain illustrative combinations of elements and/or functions, it should be appreciated that different combinations of elements and/or functions may be provided by alternative implementations without departing from the scope of the appended claims. 

I claim:
 1. A method of playing a board game having board positions presented as occupiable spaces, the method comprising: displaying a choice of selectable numeric values; performing a plurality of reiterative game operations, wherein each individual reiterative game operation of the plurality of reiterative game operations comprises having a first player select a first selectable numeric value, having a second player select a second selectable numeric value, performing a mathematical operation utilizing the first selectable numeric value and the second selectable numeric value, displaying a plurality of resulting numeric values each in one of the occupiable spaces, wherein each one of the resulting numeric values is a mathematical result of performing the mathematical operation using a unique two of the selectable numeric values, designating that occupiable space having therein the resulting numeric value particular to the first selectable numeric value and the second selectable numeric value as being occupied by the second player; performing additional ones of the reiterative operations, wherein roles of the first player and the second player are exchanged in each of the additional ones of the reiterative operations, and each of the occupiable spaces occupied by the first player and the second player is maintained as so occupied throughout each one reiterative operation, until one of the first player and the second player has occupied a predetermined array of adjacent occupiable spaces; and recognizing as a winner of each reiterative game operation that player having occupied the predetermined array of adjacent occupiable spaces, summing the number of occupied predetermined arrays for each of the players, and declaring as a winner of the game that player having the greatest number of occupied predetermined arrays.
 2. The method of claim 1, wherein at least one the selectable numeric values and at least one of the resulting numeric values comprise an integer and a symbolic value of indeterminate magnitude.
 3. The method of claim 2, wherein the step of performing a mathematical operation utilizing the first selectable numeric value and the second selectable numeric value comprises generating and solving quadratic equations.
 4. The method of claim 1, wherein the predetermined array of adjacent occupied spaces comprises three adjacent spaces of the board game arranged in a straight line.
 5. The method of claim 3, wherein the three adjacent spaces are arranged serially in a horizontal row of the board game.
 6. The method of claim 3, wherein the three adjacent spaces are arranged serially in a vertical column of the board game.
 7. The method of claim 3, wherein the three adjacent spaces are arranged serially in a diagonal row of the board game.
 8. The method of claim 1, wherein the step of performing additional ones of the reiterative operations comprises alternating respective roles of the first player and the second player in each subsequent iteration of the reiterative operations. 